Will this adapter support 1024X768 resolution via an HDMI converter?

I have a need to support a projector's native resolution of 1024X768 pixels. The HDMI port on the Mac mini only supports the video resolutions of 720 or 1080 high, and 1600X900. If I use the T'bolt port to a DVI adapter, will it support the old computer resolution standards and aspect ratio?